I would say that the bible prescribes that we let people know when they've offended us (can't think of the exact verse, but several in the new testament and in the old testament tell you to go to your brother or neighbor if they offend you, and "not suffer sin on them").
I think there's a tendency to consider forgiveness as a one sided thing. But have you really forgiven someone if they don't even know if they offended you in the first place?
There are a lot of verses in the bible that tell us to let others know if we've been wronged.
Furthermore, I've been finding a lot of healing in opening up to others if I've been offended.
I used to think that by overlooking something as if it had never happened, I was doing the right thing. But it didn't feel right to just let something go without giving the person the chance to know that they had done something wrong. In the cases where I've actually at least told the person, my conscience feels clear and my spirit feels lighter.
What does everyone else think?
Welcome to CC, Cyph!
Allow me to offer a suggestion, as you are new. It's best to do a bit of homework on the issue that you're discussing. BibleGateway.com allows you to do a keyword search in any of about 50 English translations; it's like a concordance, except that you can search for several words or a phrase rather than just a single word. That way, you're not opening the discussion with, "I think the Bible says such and such".
To the specific topic, Jesus says in Mark 11:25, "Whenever you stand praying, forgive, if you have anything against anyone, so that your Father who is in heaven will also forgive you your transgressions." Nothing is said about telling the offending person; it's a transaction between the offended and God. I'm not aware of anything in Scripture specifically commanding or recommending telling the offender and then forgiving them.
I'll use the term, "confrontation" to mean telling the offender what action has caused the transgression; it doesn't mean an unpleasant confrontation. Because there is so little in Scripture on the subjects of confronting and extending forgiveness, we need to employ some wisdom. With regard to telling the offender what they have done, it
may be appropriate. In many cases, both the offender and offended will be well aware of the transgression. In others, the offender will not accept responsibility or doesn't value being forgiven, so telling them is fruitless. Occasionally, the"offender" may actually be innocent of wrongdoing; people get mad at God, but He doesn't do anything wrong. I would suggest that if the relationship is close enough (a family member, housemate, or close neighbour), and the grievance serious enough or is a pattern of behaviour, then confronting may be appropriate. One more thought: if you do tell the offender, be specific and focus on the action, not the person, so that your confrontation is redemptive.
With regard to extending forgiveness, it depends also on the nature of the relationship and of the offense. Sometimes it can't be done; many people process offenses from the previous generation after they have died. In other cases, direct communication may be inappropriate or even impossible; for example, abused children should not attempt such communication with their abusers. Sometimes it just isn't necessary.
When Jesus died on the cross, He took the penalty for
all our sins. When we first believe the gospel, the Holy Spirit does not confront us with every sin (well, most people don't experience that). Rather, as we grow in Christ, He brings things to our attention that need processing with Him; these can be old hurts and offenses that are decades old. He doesn't intend that we reconcile every relationship, but that we reconcile the one that matters: between ourselves and Him. Forgiving others takes place, as the verse from Mark says, when you are praying. The offender need never know, but if they are aware of the transgression, your changed attitude toward them will tell them they are forgiven. Sometimes, being Christlike means carrying the weight--and consequences--of someone else's transgression and forgiving them anyway.
There is another important component to the discussion, which you didn't mention: repentance. Forgiving another does
not require that they repent first, because they may
never repent, and you are still called to forgive. Telling them their transgression and extending forgiveness with no repentance may simply lead to further transgression; God's direction in this is needed. Just remember that forgiveness frees
you, not necessarily the person you forgive.